The centre Andrew Suniula and his brother, the replacement fly-half Shalom Suniula, scored tries two minutes apart as the USA rallied from a 10-point deficit to beat Uruguay and earn a trip the Rugby World Cup in England next year.

Speaking on television after the game, the Eagles captain Todd Clever said: "I always though we'd get there. But it took longer than I expected and I'm proud of everyone in the team for sticking in there."

The Eagles took the home-and-home series after the teams drew 27-27 a week earlier, in Montevideo. Los Teros still have a chance to qualify for the finals, through the cross-continent repechage competition.

Playing before a boisterous crowd of about 5,000 at Kennesaw State University in suburban Atlanta, the Eagles had fallen behind 13-3 by the break.

Uruguay took advantage of several calls against the US from the English referee, Greg Garner, getting a try from the centre Joaquin Prada in the 22nd minute while the Americans were short-handed thanks to yellow cards shown to Suniula, for a retaliatory punch, and the replacement prop Nick Wallace, for a technical scrummaging offence.

Uruguay's fly-half, Felipe Berchesi, knocked over a couple of penalty kicks from distance; Los Teros' hooker and captain, Arturo Avalo, also spent 10 minutes of the first half off the field, thanks to a dangerous tackle which presented the US full-back Chris Wyles with the first of two penalties. The Eagles were twice held up over the line – Andrew Suniula and the wing Blaine Scully were the men in possession.

Capitalising on the superior fitness of their professional players, the US came back strongly in the second half and the tighthead prop Eric Fry – part of an Eagles front row which was again conclusively outscrummaged by its South American opponents – scored a try from short range in the 46th minute, after a strong run by the lock Samu Manoa.

Fry's try provided the first five of 29 unanswered US points; the scrum-half Mike Petri put the Eagles ahead for good in the 61st minute, taking a quick tap penalty to score, before the Suniula brothers finished off the game. Wyles kicked 12 points, with two penalties and two conversions.

The Eagles will play in Pool B in England, with South Africa, Scotland – their opponents in Houston in June – Samoa and the Asia qualifier, which will almost certainly be Japan.

At the post-match press conference in Atlanta, coach Mike Tolkin said: "We're not backing down from anyone. Our goal is to get out of the pool."